Question

find all critical numbers of f(x) = (x - 1)^2 * (x - 2)^3

Answer 1

starting with finding the derivative, I get f'(x) = 2(x-1)(x-2)^3 + 3(x-2)^2 * (x - 1)^2

Answer 2

HI!!

Answer 3

by some total miracle this actually factors as \[(x-2)^2 (x-1) (5 x-7)\] so the critical numbers are real easy to find

Answer 4

actually it is not really a miracle since you can factor out the common factor of \((x-2)^2(x-1)\) and see what you have left

Answer 5

now, I would find when the derivative would equal zero, can someone walk me through this?

Answer 6

set each factor equal to zero and solve
you do it in your head mostly

Answer 7

thanks to both of you for your help. there are connection issues here, and I was stuck as factoring as the first step.

Answer 8

so, got 1,2,7/5